Lectures On K Hler Manifolds
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Lectures On K Hler Manifolds
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Author : Werner Ballmann
language : en
Publisher: European Mathematical Society
Release Date : 2006
Lectures On K Hler Manifolds written by Werner Ballmann and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
These notes are based on lectures the author gave at the University of Bonn and the Erwin Schrodinger Institute in Vienna. The aim is to give a thorough introduction to the theory of Kahler manifolds with special emphasis on the differential geometric side of Kahler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kahler manifolds. The more advanced topics are the cohomology of Kahler manifolds, Calabi conjecture, Gromov's Kahler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on Chern-Weil theory, symmetric spaces, and $L^2$-cohomology.
Lectures On K Hler Groups
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Author : Pierre Py
language : en
Publisher: Princeton University Press
Release Date : 2025-03-25
Lectures On K Hler Groups written by Pierre Py and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-25 with Mathematics categories.
"A natural question that sits at the nexus of algebraic geometry, differential geometry, and geometric group theory is: which groups can be realized as fundamental groups of compact Kähler manifolds, called "Kähler groups"? Roughly speaking, the fundamental group of a manifold measures the number of "holes." Many restrictions are known, and many examples are known; but mathematicians are far from having a precise conjecture about which groups are Kähler. The question serves as a fruitful connection between several major areas of geometry and complex analysis. Py's book is an up-to-date pedagogical survey of the central theorems and methods for the study of Kähler groups including, where illuminating, detailed proofs. It includes results of Gromov, Schoen, Napier, Ramachandran, Corlette, Simpson, Delzant, Arapura, and Nori. The charm of the subject is that different methods yield information of different flavors, and the challenge is to draw these threads together. This book leans toward geometric group theory, but it gives a coherent account of great value to anyone interested in Kähler groups - and in Kähler manifolds more broadly. The emphasis is on unity and cross-fertilization among approaches"--
Lectures On K Hler Geometry
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Author : Andrei Moroianu
language : en
Publisher: Cambridge University Press
Release Date : 2007-03-29
Lectures On K Hler Geometry written by Andrei Moroianu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-29 with Mathematics categories.
Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.
Lectures On K Hler Groups
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Author : Pierre Py
language : en
Publisher: Princeton University Press
Release Date : 2025-03-25
Lectures On K Hler Groups written by Pierre Py and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-25 with Mathematics categories.
An introduction to the state of the art in the study of Kähler groups This book gives an authoritative and up-to-date introduction to the study of fundamental groups of compact Kähler manifolds, known as Kähler groups. Approaching the subject from the perspective of a geometric group theorist, Pierre Py equips readers with the necessary background in both geometric group theory and Kähler geometry, covering topics such as the actions of Kähler groups on spaces of nonpositive curvature, the large-scale geometry of infinite covering spaces of compact Kähler manifolds, and the topology of level sets of pluriharmonic functions. Presenting the most important results from the past three decades, the book provides graduate students and researchers with detailed original proofs of several central theorems, including Gromov and Schoen’s description of Kähler group actions on trees; the study of solvable quotients of Kähler groups following the works of Arapura, Beauville, Campana, Delzant, and Nori; and Napier and Ramachandran’s work characterizing covering spaces of compact Kähler manifolds having many ends. It also describes without proof many of the recent breakthroughs in the field. Lectures on Kähler Groups also gives, in eight appendixes, detailed introductions to such topics as the study of ends of groups and spaces, groups acting on trees and Hilbert spaces, potential theory, and L2 cohomology on Riemannian manifolds.
Lectures On Hyperhamiltonian Dynamics And Physical Applications
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Author : Giuseppe Gaeta
language : en
Publisher: Springer
Release Date : 2017-07-21
Lectures On Hyperhamiltonian Dynamics And Physical Applications written by Giuseppe Gaeta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-21 with Science categories.
This book provides the mathematical foundations of the theory of hyperhamiltonian dynamics, together with a discussion of physical applications. In addition, some open problems are discussed. Hyperhamiltonian mechanics represents a generalization of Hamiltonian mechanics, in which the role of the symplectic structure is taken by a hyperkähler one (thus there are three Kähler/symplectic forms satisfying quaternionic relations). This has proved to be of use in the description of physical systems with spin, including those which do not admit a Hamiltonian formulation. The book is the first monograph on the subject, which has previously been treated only in research papers.
Lectures On Symplectic Geometry
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Author : Ana Cannas da Silva
language : en
Publisher: Springer
Release Date : 2004-10-27
Lectures On Symplectic Geometry written by Ana Cannas da Silva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-27 with Mathematics categories.
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
K Hler Immersions Of K Hler Manifolds Into Complex Space Forms
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Author : Andrea Loi
language : en
Publisher: Springer
Release Date : 2018-09-20
K Hler Immersions Of K Hler Manifolds Into Complex Space Forms written by Andrea Loi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-20 with Mathematics categories.
The aim of this book is to describe Calabi's original work on Kähler immersions of Kähler manifolds into complex space forms, to provide a detailed account of what is known today on the subject and to point out some open problems. Calabi's pioneering work, making use of the powerful tool of the diastasis function, allowed him to obtain necessary and sufficient conditions for a neighbourhood of a point to be locally Kähler immersed into a finite or infinite-dimensional complex space form. This led to a classification of (finite-dimensional) complex space forms admitting a Kähler immersion into another, and to decades of further research on the subject. Each chapter begins with a brief summary of the topics to be discussed and ends with a list of exercises designed to test the reader's understanding. Apart from the section on Kähler immersions of homogeneous bounded domains into the infinite complex projective space, which could be skipped without compromising the understanding of the rest of the book, the prerequisites to read this book are a basic knowledge of complex and Kähler geometry.
Lectures On Set Theoretic Topology
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Author : Mary Ellen Rudin
language : en
Publisher: American Mathematical Soc.
Release Date : 1975-12-31
Lectures On Set Theoretic Topology written by Mary Ellen Rudin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-12-31 with Mathematics categories.
This survey presents some recent results connecting set theory with the problems of general topology, primarily giving the applications of classical set theory in general topology and not considering problems involving large numbers. The lectures are completely self-contained--this is a good reference book on modern questions of general topology and can serve as an introduction to the applications of set theory and infinite combinatorics.
Lectures On The L2 Sobolev Theory Of The D Bar Neumann Problem
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Author : Emil J. Straube
language : en
Publisher: European Mathematical Society
Release Date : 2010
Lectures On The L2 Sobolev Theory Of The D Bar Neumann Problem written by Emil J. Straube and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This book provides a thorough and self-contained introduction to the $\bar{\partial}$-Neumann problem, leading up to current research, in the context of the $\mathcal{L}^{2}$-Sobolev theory on bounded pseudoconvex domains in $\mathbb{C}^{n}$. It grew out of courses for advanced graduate students and young researchers given by the author at the Erwin Schrodinger International Institute for Mathematical Physics and at Texas A & M University. The introductory chapter provides an overview of the contents and puts them in historical perspective. The second chapter presents the basic $\mathcal{L}^{2}$-theory. Following is a chapter on the subelliptic estimates on strictly pseudoconvex domains. The two final chapters on compactness and on regularity in Sobolev spaces bring the reader to the frontiers of research. Prerequisites are a solid background in basic complex and functional analysis, including the elementary $\mathcal{L}^{2}$-Sobolev theory and distributions. Some knowledge in several complex variables is helpful. Concerning partial differential equations, not much is assumed. The elliptic regularity of the Dirichlet problem for the Laplacian is quoted a few times, but the ellipticity results needed for elliptic regularization in the third chapter are proved from scratch.
Lectures On Differential Geometry
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Author : Bennett Chow
language : en
Publisher: American Mathematical Society
Release Date : 2024-09-23
Lectures On Differential Geometry written by Bennett Chow and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Mathematics categories.
Differential geometry is a subject related to many fields in mathematics and the sciences. The authors of this book provide a vertically integrated introduction to differential geometry and geometric analysis. The material is presented in three distinct parts: an introduction to geometry via submanifolds of Euclidean space, a first course in Riemannian geometry, and a graduate special topics course in geometric analysis, and it contains more than enough content to serve as a good textbook for a course in any of these three topics. The reader will learn about the classical theory of submanifolds, smooth manifolds, Riemannian comparison geometry, bundles, connections, and curvature, the Chern?Gauss?Bonnet formula, harmonic functions, eigenfunctions, and eigenvalues on Riemannian manifolds, minimal surfaces, the curve shortening flow, and the Ricci flow on surfaces. This will provide a pathway to further topics in geometric analysis such as Ricci flow, used by Hamilton and Perelman to solve the Poincar‚ and Thurston geometrization conjectures, mean curvature flow, and minimal submanifolds. The book is primarily aimed at graduate students in geometric analysis, but it will also be of interest to postdoctoral researchers and established mathematicians looking for a refresher or deeper exploration of the topic.